Geometric techniques for implicit two-dimensional systems

Geometric tools are developed for two-dimensional (2-D) models in an implicitFornasini–Marchesini form. In particular, the structural properties of controlled and conditionedinvariance are defined and studied. These properties are investigated in terms ofquarter-plane causal solutions of the implicit model given compatible boundary conditions.The definitions of controlled and conditioned invariance introduced, along with the correspondingoutput-nulling and input-containing subspaces, are shown to be richer than theone-dimensional counterparts. The analysis carried out in this paper establishes necessaryand sufficient conditions for the solvability of 2-D disturbance decoupling problems andunknown-input observation problems. The conditions obtained are expressed in terms ofoutput-nulling and input-containing subspaces, which can be computed recursively in a finitenumber of steps

A Novel MIMO Control for Interleaved Buck Converters in EV DC Fast Charging Applications

This brief proposes a new multiple input multiple output (MIMO) control for off-board electric vehicle (EV) dc fast chargers. The proposed feedback matrix design avoids multiple tuning of controllers in multiple and interconnected loops while improving the performance of interleaved dc buck converters over classical PI/PID controls. The innovative features of the presented strategy are the reference current monotonic tracking from any initial state of charge with an arbitrarily fast settling time and the fast compensation of both load variations and imbalances among the legs. Numerical results validate the performance improvements of the proposed discrete-time MIMO algorithm for interleaved buck converters over classical PI/PID controls. Full-scale hardware-in-the-loop (HIL) and scaled-down prototype experimental results prove the feasibility and effectiveness of the proposal

Detectability subspaces and observer synthesis for two-dimensional systems

The notions of input-containing and detectability subspaces are developed within the context of observer synthesis for two-dimensional (2-D) Fornasini-Marchesini models. Specifically, the paper considers observers which asymptotically estimate the local state, in the sense that the error tends to zero as the reconstructed local state evolves away from possibly mismatched boundary values, modulo a detectability subspace. Ultimately, the synthesis of such observers in the absence of explicit input information is addressed

Squaring Down LTI Systems: A Geometric Approach

In this paper, the problem of reducing a given LTI system into a left or right invertible one is addressed and solved with the standard tools of the geometric control theory. First, it will be shown how an LTI system can be turned into a left invertible system, thus preserving key system properties like stabilizability, phase minimality, right invertibility, relative degree and infinite zero structure. Moreover, the additional invariant zeros introduced in the left invertible system thus obtained can be arbitrarily assigned in the complex plane. By duality, the scheme of a right inverter will be derived straightforwardly. Moreover, the squaring down problem will be addressed. In fact, when the left and right reduction procedures are applied together, a system with an unequal number of inputs and outputs is turned into a square and invertible system. Furthermore, as an example it will be shown how these techniques may be employed to weaken the standard assumption of left invertibility of the plant in many optimization problems

On the exact solution of the matrix Riccati differential equation

In this paper we establish explicit closed formulae for the solution of the matrix Riccati differential equation (RDE) with a terminal condition that that involve particular solutions of the associated algebraic Riccati equation. We discuss how these formulae change as assumptions are progressively weakened

New Results in Singular Linear Quadratic Optimal Control

This paper focuses on the singular infinite-horizon linear quadratic (LQ) optimal control problem for continuous-time systems. In particular, we are interested in the stabilising impulse-free solutions to this problem that can be expressed as a static state feedback. In particular we establish a link between the geometric properties of the so-called Hamiltonian system associated with the optimal control problem at hand and the so-called proper deflating subspaces of the Hamiltonian matrix pencil

A straightforward approach to the cheap LQ poblem for continuous-time systems in geometric terms

This paper addresses the cheap version of the classical linear quadratic (LQ) optimal control problem for continuous-time systems. The approach herein considered differs from those presented in literature, since it consists of applying the tools of the geometric control theory to the Hamiltonian system. In this way, it is possible to compute the stabilizing state-feedback gain achieving optimality by using standard geometric algorithms, whenever the initial state satisfies a suitable necessary and sufficient condition for solvability, also stated in geometric terms